CREATE TABLE gps_subgroup_data (
	ambient	text,	-- The {{KNOWL('group.label', 'label')}} of the {{KNOWL('group.ambient', 'ambient group')}}
	aut_centralizer_order	numeric,	-- (description not yet updated on this server)
	aut_label	text,	-- (description not yet updated on this server)
	aut_quo_index	numeric,	-- (description not yet updated on this server)
	aut_stab_index	numeric,	-- (description not yet updated on this server)
	aut_weyl_group	text,	-- (description not yet updated on this server)
	aut_weyl_index	numeric,	-- (description not yet updated on this server)
	centralizer	text,	-- The {{KNOWL('group.subgroup_label', 'short label')}} of the {{KNOWL('group.centralizer', 'centralizer')}} of the subgroup
	complements	_text,	-- The {{KNOWL('group.complement', 'complements')}} of this subgroup.  An empty list if not {{KNOWL('columns.gps_subgroups.split', 'split')}}
	conjugacy_class_count	numeric,	-- The number of conjugacy classes in this equivalence class.  If {{KNOWL('columns.gps_subgroups.outer_equivalence', 'outer_equivalence')}} is false this will just be 1.
	contained_in	_text,	-- {{KNOWL('group.subgroup_label', 'short labels')}} for the subgroups containing this subgroup (up to conjugacy or automorphism, as determined by the value of {{KNOWL('columns.gps_subgroups.outer_equivalence', 'outer_equivalence')}})
	contains	_text,	-- {{KNOWL('group.subgroup_label', 'short labels')}} for the subgroups containing this subgroup (up to conjugacy or automorphism, as determined by the value of {{KNOWL('columns.gps_subgroups.outer_equivalence', 'outer_equivalence')}})
	core	text,	-- The {{KNOWL('group.subgroup_label', 'short label')}} of the {{KNOWL('group.core', 'core')}} of the subgroup
	coset_action_label	text,	-- For subgroups with trivial {{KNOWL('group.core', 'core')}}, the {{KNOWL('gg.label', 'transitive group label')}} for the faithful transitive action of the ambient group on the cosets of the subgroup
	count	numeric,	-- The number of subgroups in this equivalence class.  If {{KNOWL('columns.gps_subgroups.outer_equivalence', 'outer_equivalence')}} is true this will be the number of subgroups {{KNOWL('group.autjugate_subgroup', 'autjugate')}} to the given one, otherwise it will be the number of subgroups conjugate to the given one.
	diagramx	_int2,	-- x-coordinates for this subgroup in various subgroup lattice layouts
	generators	_numeric,	-- (description not yet updated on this server)
	id	bigint,	-- 
	label	text,	-- The {{KNOWL('group.subgroup_label', 'label')}} of the subgroup
	mobius_quo	bigint,	-- The value of the {{KNOWL('group.mobius_function', 'möbius quotient function')}} on this subgroup.
	mobius_sub	bigint,	-- The value of the {{KNOWL('group.mobius_function', 'möbius subgroup function')}} on this subgroup.
	normal_closure	text,	-- The {{KNOWL('group.subgroup_label', 'short label')}} of the {{KNOWL('group.subgroup.normal_closure', 'normal closure')}} of the subgroup
	normal_contained_in	_text,	-- (description not yet updated on this server)
	normal_contains	_text,	-- (description not yet updated on this server)
	normalizer	text,	-- The {{KNOWL('group.subgroup_label', 'short label')}} of the {{KNOWL('group.subgroup.normalizer', 'normalizer')}} of the subgroup
	old_label	text,	-- previous label before making canonical
	projective_image	text,	-- The {{KNOWL('group.label', 'label')}} of the image of this subgroup in the {{KNOWL('group.central_quotient', 'central quotient')}} of the {{KNOWL('group.ambient', 'ambient group')}}
	quotient_action_image	text,	-- The {{KNOWL('group.label', 'label')}} of the image of the map from the quotient to the automorphism group of the subgroup.  NULL if the subgroup is not {{KNOWL('group.subgroup.normal', 'normal')}} and either {{KNOWL('group.subgroup.split', 'split')}} or {{KNOWL('group.abelian', 'abelian')}}.
	quotient_action_kernel	text,	-- The {{KNOWL('group.label', 'label')}} of the kernel of the map from the quotient to the automorphism group of the subgroup.  NULL if the subgroup is not {{KNOWL('group.subgroup.normal', 'normal')}} and either {{KNOWL('group.subgroup.split', 'split')}} or {{KNOWL('group.abelian', 'abelian')}}.
	quotient_action_kernel_order	numeric,	-- The {{KNOWL('group.order', 'order')}} of the {{KNOWL('columns.gps_subgroups.quotient_action_kernel', 'quotient_action_kernel')}}
	quotient_fusion	jsonb,	-- Not yet computed.  The intention is to store how conjugacy classes fuse when passing from the ambient group to the quotient
	short_label	text,	-- (description not yet updated on this server)
	subgroup_fusion	_int4,	-- Not yet computed.  The intention is to store how conjugacy classes fuse when passing from subgroup to the ambient group
	weyl_group	text 	-- (description not yet updated on this server)
);